I don't think you can get past this even if he doesn't go.
YANBU, he shouldn't want to go.
My DH missed our 1st as he was born at 36 weeks and 5 days by emergency CS as I suddenly developed preeclampsia at 36 weeks.
He was away with work (not by choice) and was only allowed 4 weeks off, so he'd originally booked to be off from the 38th week.
As soon as I was admitted to hospital, treated and then told I was stable, we talked and I said things would be okay and I'd see him as planned, but he still changed his flight to the earliest reasonably priced one he could get (5 days away).
On day 4, the doctors said I was well enough to be discharged the next morning as things seemed to be improving.
That night, though, things suddenly deteriorated very rapidly, and as soon as he knew what was happening he drove to the nearest airport and tried to get a flight.
The earliest he could find was for 6am the next day, and even though it cost a fortune and I was telling him to just catch his already booked flight at 7pm that next day, he booked it and got to me as quick as he could.
I had my family with me so I wasn't alone.
Unfortunately, the drugs they'd given me to try to stabilise me and avoid surgery didn't work and I was rushed in for a CS at 8am, so he ended up missing the birth by about 2 hours, but at least he tried.
I guess the point I'm making is that he didn't miss it deliberately and even though I said I'd be fine alone, he wanted to be there for us and did what he could to make sure that happened, which did make me feel cherished/ important, and that's what your husband should be doing.
Whereas in reality, he doesn't seem to be bothered; it's all about his wants and his needs, and he's trying to guilt you into agreeing with him.
Think back to whether or not he's shown these traits before, and you've ignored it? Especially as you've said he sulks, so I can imagine you might try to avoid that. If it is a pattern of behaviour, he's unlikely to change.
So sorry. Hope you're OK. 💐